You can go to any clinic in the UK. All you have to give is a name (doesnt have to be your own), and a phone number. You dont have to give date of birth or address (or you can make up a DOB) and you dont have to give personal details about your risk.
BUT.... their questions pertain to your risk, so they know what to test you for and things to look out for. If for example you like going around having unprotected bum fun then chances are they are going to do a hell of a lot more testing on you than someone who likes to stick their nob in carrier bags and watch babestation on tv.
Ultimately, they have heard it all, seen it all, it makes no difference the staff there, your just another number so there is no need to be embarrassed at all.
If you dont want to go a GUM clinic near you, travel and go to one in a town away from you. Alternatively, get home tests. A clamydia and gonnoreah home testing kit from Better2Know is only £40 and results are back within 3 days. You can get home HIV tests from places like Superdrug, Lloyds Pharmacy now for £30, there really is no excuse for not testing, and you can have these kits sent to other addresses, they come in plain packaging etc.
As for how you are notified, GUM clinics will contact you using your preferred method, most usually ask for 2, I have given them my email address and phone number, usually they will then drop you a text within 10 days saying all clear, or please call us.
Yes the private clinics give much faster service and usually you are on your own in the waiting rooms. But you pay the price of the tests which can be £300-£400 upwards for a full set of STI testing.
Really, really is no excuse.